The present invention relates to (a) novel fluorine-containing monomers having a special structure, that is, a hydroxyl group or a substituent for protecting or modifying hydroxyl group, (b) polymers prepared by polymerization or copolymerization of such monomers, and (c) materials (e.g., reflection preventive materials, photosensitive coatings, and resist materials) containing such polymers.
Fluorine-containing compounds have been used and developed in various fields particularly in the field of advanced materials due to their good qualities (e.g., water repellency, oil repellency, low water absorption, heat resistance, weather resistance, corrosion resistance, transparency, photosensitivity, low refractive index, and low dielectric property). In particular, there have been active researches and developments of fluorine-containing compounds in the fields of (a) reflection preventive films utilizing low refractive index and visible light transparency of fluorine-containing compounds, (b) optical devices utilizing transparency of fluorine-containing compounds in a long wavelength band for optical communication, and (c) resist materials utilizing transparency of fluorine-containing compounds in ultraviolet region (particularly vacuum ultraviolet wavelength region). In these fields, the common task of designing polymers is to achieve adhesion to the substrate and high glass transition point (hardness), while achieving transparency at each wavelength for use by introducing as many fluorine atoms as possible into the polymer. Although there have been various proposals for increasing transparency at each wavelength by increasing the fluorine content in the polymer, there is no or very few proposals for improving water repellency and adhesion and for obtaining higher glass transition point by newly designing fluorine-containing monomers themselves. Recently, there have been some reports of hydroxyl group-containing and fluorine-containing styrenes and hydroxyl group-containing and fluorine-containing norbornene compounds in the field of the next generation F2 resist in vacuum ultraviolet region. However, there are demands for new materials (i.e., novel polymers and novel monomers for providing novel polymers) having a sufficiently low refractive index necessary for reflection preventive films, for those having a sufficient transparency at optical communication wavelength, and for those having both of a sufficient transparency in ultraviolet region and a sufficient etching resistance.
It is an object of the present invention to provide a novel polymerizable monomer capable of providing polymers that have (a) high transparency in a wide wavelength region from vacuum ultraviolet region to optical communication wavelength region, (b) improved adhesion to the substrate, and (c) improved film forming property.
According to the present invention, there is provided a polymerizable monomer represented by the general formula (1), 
wherein R1 is a hydrogen atom, a halogen atom, a hydrocarbon group or a fluorine-containing alkyl group;
R2 is a straight-chain or branched alkyl group, a cyclic alkyl group, an aromatic group, or a substituent having at least two of these groups, said R2 being optionally partially fluorinated;
R3 is a hydrogen atom, a hydrocarbon group that is optionally branched, a fluorine-containing alkyl group, or a cyclic group having an aromatic or alicyclic structure, said R3 optionally containing a bond of an oxygen atom or carbonyl group; and
n is an integer of 1-2.
The above-mentioned novel polymerizable monomer according to the present invention is a fluorine-containing acrylate derivative having a high fluorine content and a hydroxyl group or a substituent (R3) for protecting or modifying the hydroxyl group. The inventors unexpectedly found that polymers prepared by polymerization or copolymerization using the novel polymerizable monomer have (a) high transparency in a wide wavelength region from vacuum ultraviolet region to optical communication wavelength region, (b) improved adhesion to the substrate, and (c) improved film forming property. Therefore, the resulting polymers are very useful for reflection preventive materials, optical device materials and resist materials. Furthermore, the polymerizable monomer, which is an acrylic monomer, is easy to be handled in an industrial scale production.
The novel polymerizable monomer, represented by the general formula (1), has fluorine and hydroxyl group coexistent in its hexafluoroisopropanol group. As defined above, R1 usable in the general formula (1) can be selected from hydrogen atom, halogen atoms, hydrocarbon groups and fluorine-containing alkyl groups. Of these, preferable halogen atoms are fluorine, chlorine and bromine. Preferable hydrocarbon groups are methyl group, ethyl group, propyl group, isopropyl group, butyl group, isobutyl group, sec-butyl group, tert-butyl group, cyclopentyl group, cyclohexyl group, phenyl group, benzyl group, and phenethyl group. Examples of the fluorine-containing alkyl groups are those containing fluorine atom partially or totally substituted for hydrogen atom of the above-cited alkyl groups. In the case of the hydrocarbon groups and the fluorine-containing alkyl groups, the number of carbon atoms in the molecule is preferably about 1-20, preferably 1-4 from the viewpoint of polymerizability of the monomer. Exemplary fluorine-containing groups are trifluoromethyl group (xe2x80x94CF3), trifluoroethyl group (xe2x80x94CH2CF3), 1,1,1,3,3,3-hexafluoroisopropyl group, heptafluoroisopropyl group, and nonafluoro-n-butyl group (xe2x80x94C4F9).
As stated above, R2 usable in the general formula (1) can be a straight-chain or branched alkyl group, a cyclic alkyl group, an aromatic group, or a substituent having at least two of these groups. Furthermore, R2 is optionally partially fluorinated and optically contains an unsaturated bond(s). Examples of R2 are straight-chain or branched alkylene groups such as methylene group, ethylene group, isopropylene group and t-butylene group; cyclic groups such as cyclobutene group, cyclohexane group, norbornene group and adamantane group; and aromatic groups such as phenyl group.
Specific examples of the polymerizable monomer (represented by the general formula (1)) are represented by the following general formulas (2)-(5): 
wherein R3 is a hydrogen atom, a hydrocarbon group that is optionally branched, a fluorine-containing alkyl group, or a cyclic group having an aromatic or alicyclic structure, and R3 optionally contains a bond of an oxygen atom or carbonyl group. If R3 is a hydrogen atom, the resulting polymer is improved in transparency. However, depending on the use of the resulting polymer, R3 can be selected from the other groups. Examples of such groups are hydrocarbon groups having a carbon atom number of about 1-20 and optionally having a cyclic structure, such as methyl group, ethyl group, isopropyl group, cyclopropyl group, cyclopentyl group, cyclohexyl group, norbornel group, adamantyl group and benzyl group. Further exemplary oxygen atom-containing groups are open-chain ether groups such as methoxymethyl ether and methoxyethoxymethyl ether; cyclic ether groups such as tetrahydrofuran and tetrahydropyrane; and aromatic groups such as 4-methoxybenzyl group. Further exemplary carbonyl-containing groups are acetyl group, pivaloyl group, tert-butoxycarbonyl group, and benzoyl group. It is possible to protect or modify the carbonyl-containing groups. Its purpose is to provide the polymers, for example, with (a) crosslinking property, (b) positive-type photosensitivity by a photo-induced acid generator, and (c) etching resistance, thereby producing the polymers having a good solubility in organic solvents and alkali aqueous solutions, a high glass transition point, and a heat resistance upon soldering. Thus, R3 can suitably be selected depending on the use of the polymer.
R4 in the general formula (3) can be a hydrocarbon group having a carbon atom number of 1-20. Its examples are open-chain hydrocarbon groups such as methylene, ethylene and isopropylene; and cyclic hydrocarbon groups such as cyclopropyl, cyclopentyl, cyclohexyl and norbornel and adamantyl. The hydrocarbon group may be partially replaced with, for example, fluorine, bromine and chlorine. Further exemplary oxygen-containing groups are C3-C5 cyclic ethers, C1-C20 straight-chain or branched alkyl groups. Further exemplary aromatic groups are phenyl group, diphenyl ether group, trifluoromethylphenyl group, and ditrifluoromethylphenyl groups. Furthermore, R4 may have an unsaturated bond(s).
R5 in the general formulas (4) and (5) can be a hydrocarbon group having a carbon atom number of 1-5. Its examples are open-chain hydrocarbon groups such as methylene, ethylene, isopropylene, butylene, isobutylene, and sec-butylene; and cyclic hydrocarbon groups such as cyclopropyl, cyclopentyl, cyclohexyl, norbornel, and adamantyl.
The method for synthesizing the xcex1, xcex2-unsaturated esters, which are represented by the general formulas (1)-(5), is not particularly limited. For example, they can be synthesized by a condensation of an alcohol (derived from hexafluoroacetone) with an xcex1, xcex2-unsaturated carboxyl acid (e.g., acrylic acid, methacrylic acid, 2-trifluoromethyl acrylic acid, 2-nonafluoro-n-buthyl acrylic acid) or xcex1, xcex2-unsaturated carboxylic halide (e.g., acrylic chloride, methacrylic chloride, 2-trifluoromethylacrylic chloride, and 2-nonafluoro-n-butylacrylic chloride). As another example, they can be synthesized by an addition reaction of a double bond-containing compound (derived from hexafluoroacetone) with an xcex1, xcex2-unsaturated carboxylic acid (e.g., acrylic acid, methacrylic acid, 2-trifluoromethylacrylic acid, and 2-nonafluoro-n-butylacrylic acid) in the presence of a Lewis acid (e.g., sulfuric acid, hydrochloric acid, methanesulfonic acid, and trifluoromethanesulfonic acid).
The reaction product after each reaction can be purified by a known method such as concentration, distillation, extraction, recrystallization, filtration, and column chromatography. It is optional to combine at least two of the purification procedures.
The polymer according to the present invention can be (a) a homopolymer prepared by polymerizing one of the above-mentioned polymerizable monomers represented by the general formulas (1)-(5), or (b) a copolymer prepared by copolymerizing at least two of the polymerizable monomers represented by the general formulas (1)-(5), or (c) another copolymer prepared by copolymerizing at least one of the polymerizable monomers represented by the general formulas (1)-(5) with another comonomer.
The another comonomer is preferably at least one selected from olefins, fluorine-containing olefins, acrylic esters, methacrylic esters, fluorine-containing acrylic esters, fluorine-containing methacrylic esters, norbornene compounds, fluorine-containing norbornene compounds, styrene compounds, fluorine-containing styrene compounds, vinyl ethers, and fluorine-containing vinyl ethers.
Exemplary olefins for the another comonomer are ethylene and propylene. Exemplary fluorine-containing olefins for that are vinyl fluoride, vinylidene fluoride, trifluoroethylene, chlorotrifluoroethylene, tetrafluoroethylene, hexafluoropropylene, and hexafluoroisobutene.
Exemplary (meth)acrylic esters (i.e., acrylic esters and methacrylic esters) for that are not particularly limited with respect to their ester side chains. They are (meth)acrylic alkyl esters such as methyl (meth)acrylate, ethyl (meth)acrylate, n-propyl (meth)acrylate, isopropyl (meth)acrylate, n-butyl (meth)acrylate, isobutyl (meth)acrylate, n-hexyl (meth)acrylate, n-octyl (meth)acrylate, 2-ethylhexyl (meth)acrylate, lauryl (meth)acrylate, 2-hydroxyethyl (meth)acrylate, and 2-hydroxypropyl (meth) acrylate; (meth) acrylates containing groups such as ethylene glycol, propylene glycol and tetramethylene glycol; unsaturated amides such as (meth)acrylic amide, N-methylol(meth)acrylic amide, and diacetone acrylic amide; (meth) acrylonitrile, alkoxysilane-containing vinyl silanes and (meth)acrylic esters, t-butyl (meth)acrylate, and cyclic (meth)acrylate such as 3-oxocyclohexyl (meth)acrylate, adamantyl (meth)acrylate, alkyladamantyl (meth) acrylate, cyclohexyl (meth)acrylate, tricyclodecanyl (meth)acrylate and (meth)acrylate having cyclic structures such as lactone ring and norbornene ring; and (meth)acrylic acid. Further examples are xcex1-cyano group-containing (meth)acrylate and analogous compounds such as maleic acid, fumaric acid and maleic anhydride.
The fluorine-containing (meth)acrylic esters may have a fluorine-containing group at their xcex1-position or ester moiety. Furthermore, they may have a cyano group at the xcex1-position. Such fluorine-containing groups at their xcex1-position may be trifluoromethyl group, trifluoroethyl group and nonafluoro-n-butyl group.
Further exemplary fluorine-containing (meth)acrylic esters may have at their ester moiety a fluoroalkyl or perfluoroalkyl group or a fluorine-containing cyclic structure. This cyclic structure may have a substituent (e.g., fluorine and trifluoromethyl group), and its examples are fluorine-containing benzene ring, fluorine-containing cyclopentane ring, fluorine-containing cyclohexane ring, and fluorine-containing cycloheptane ring. Further exemplary (meth)acrylic esters may have at their ester moiety a fluorine-containing t-butyl ester group. Concrete examples of the fluorine-containing (meth)acrylic ester are 2,2,2-trifluoroethyl(meth)acrylate, 2,2,3,3-tetrafluoropropyl(meth)acrylate, 1,1,1,3,3,3-hexafluoroisopropyl(meth)acrylate, heptafluoroisopropyl(meth)acrylate, 1,1-dihydroheptafluoro-n-butyl(meth)acrylate, 1,1,5-trihydrooctafluoro-n-pentyl(meth)acrylate, 1,1,2,2-tetrahydrotridecafluoro-n-octyl(meth)acrylate, 1,1,2,2-tetrahydroheptadecafluoro-n-decyl(meth)acrylate, perfluorocyclohexylmethylacrylate, and perfluorocyclohexylmethylmethacrylate.
The above-mentioned norbornene compounds and fluorine-containing norbornene compounds may have a mononucleus or multinucleus structure. It is possible to copolymerize these norbornene compounds with the above-mentioned polymerizable monomers represented by the general formulas (1)-(5), without any particular limitations. It is preferable to prepare the norbornene compounds by a Diels-Alder addition reaction of unsaturated compounds (e.g., allyl alcohol, fluorine-containing allyl alcohol, acrylic acid, xcex1-fluoroacrylic acid, methacrylic acid, and all of the above-mentioned (meth)acrylic esters and fluorine-containing (meth)acrylic esters) to dienes (e.g., cyclopentadiene and cyclohexadiene).
Further examples of the above-mentioned another comonomer are styrene compounds and fluorine-containing styrene compounds, such as styrene, fluorinated styrene, hydroxystyrene, hexafluoroacetone-added styrene compounds, and styrene and hydroxystyrene each containing trifluoromethyl group substituted for hydrogen. These styrene compounds and fluorine-containing styrene compounds may have at their xcex1-position a halogen, an alkyl group or a fluorine-containing alkyl group.
Still further examples of the above-mentioned another comonomer are vinyl ethers, fluorine-containing vinyl ethers, allyl ethers, vinyl esters, and vinyl silanes. It is possible to copolymerize vinyl ethers, fluorine-containing vinyl ethers, allyl ethers and vinyl esters with the polymerizable monomers (represented by the general formulas (1)-(5)) by suitably adjusting relative amounts of these monomers and comonomers used in the copolymerization. For example, the another comonomer may be an alkyl vinyl ether that optionally contains methyl group, ethyl group or hydroxy group (e.g., hydroxyethyl group and hydroxybutyl group) and that optionally contains fluorine substituted for a part or all of the hydrogen atoms. The another comonomer may be cyclohexyl vinyl ether or another cyclic vinyl ether containing hydrogen or carbonyl bond in its cyclic structure. Such cyclic vinyl ether may contain fluorine substituted for a part or all of the hydrogen atoms. Furthermore, allyl ethers, vinyl esters and vinyl silanes for the another comonomer can be selected from known compounds without any particular limitation upon use.
It is optional to use a single comonomer or a combination of at least two comonomers. Upon the polymerization, the ratio of the polymerizable monomer to the another comonomer is not particularly limited. The amount of the former is preferably from 10-100%, more preferably 30-100%. If it is less than 30%, the resulting polymer may become insufficient in transparency or film-forming property depending on the wavelength range for use.
The polymerization or copolymerization method for obtaining the target polymer is not particularly limited. For example, it is preferable to use radical polymerization or ionic polymerization. In some cases, it is also possible to use coordinated anionic polymerization or living anionic polymerization.
Particulars of the above-mentioned radical polymerization are as follows. The radical polymerization can be conducted by a known manner such as bulk polymerization, solution polymerization, suspension polymerization or emulsion polymerization by a batch-wise, half-continuous or continuous operation.
The radical polymerization initiator is not particularly limited. Its examples are azo compounds, peroxides and redox compounds. Of these, azobisbutyronitrile, t-butylperoxypivalate and benzoyl peroxide are preferable.
The reaction vessel for conducting the polymerization (copolymerization) is not particularly limited. It is optional to use a solvent for conducting the polymerization. The polymerization solvent is preferably one that does not interfere with the radical polymerization. Its typical examples are esters such as ethyl acetate and n-butyl acetate; ketones such as acetone and methyl isobutyl ketone; hydrocarbons such as toluene and cyclohexane; and alcohols such as isopropyl alcohol and ethylene glycol monomethyl ether. Furthermore, it can be selected from various other solvents such as water, ethers, cyclic ethers, fluorohydrocarbons, and aromatic solvents. It is optional to use a single solvent or a mixture of at least two solvents. Furthermore, it is possible to use a molecular weight adjusting agent, such as mercaptan, in the polymerization. The temperature for conducting the polymerization may be suitably adjusted depending on the type of radical polymerization initiator or radical polymerization initiating source. It is preferably 20-200xc2x0 C., particularly preferably 30-140xc2x0 C.
After the polymerization, it is possible to remove the reaction medium (i.e., organic solvent or water) from the solution or dispersion of the target polymer by a known method. For example, it can be conducted by reprecipitation followed by filtration, or by heating under vacuum to distill the medium off.
The target polymer according to the present invention may have a number average molecular weight of 1,000-100,000, preferably 3,000-50,000.
The polymer according to the present invention may be formed into a film by dissolving the polymer in a solvent to prepare a coating solution and then by applying the coating solution to a substrate. This solvent is not particularly limited as long as the polymer can be dissolved therein. Its examples are ketones such as acetone, methyl ethyl ketone, cyclohexanone, methyl isoamyl ketone and 2-heptanone; polyhydric alcohols such as ethylene glycol, ethylene glycol monoacetate, diethylene glycol, diethylene glycol monoacetate, propylene glycol, propylene glycol monoacetate, dipropylene glycol, and ethers (monomethyl ether, monoethyl ether, monopropyl ether, monobutyl ether and monophenyl ether) of dipropylene glycol monoacetate, and derivatives of polyhydric alcohols; cyclic ethers such as dioxane; esters such as methyl lactate, ethyl lactate, methyl acetate, ethyl acetate, butyl acetate, methyl pyruvate, ethyl pyruvate, methyl methoxypropionate, and ethyl ethoxypropionate; aromatic solvents such as xylene and toluene; and fluorine-containing solvents such as fleon, alternative fleon, perfluoro compounds, and hexafluoroisopropyl alcohol. Furthermore, it is possible to use a high-boiling-point, weak solvent (e.g., a perpene-based petroleum naphtha solvent or paraffinic solvent) for the purpose of increasing coatability (applicability of the coating solution). The solvent for preparing the coating solution may be a single solvent or a mixture of at least two solvents.
It is possible to form a reflection preventive film on the surface of a substrate (e.g., glass, plastic, liquid crystal panel, plasma display panel, and electroluminescence panel) by applying the polymer of the present invention thereto to have an ultra-thin thickness. The reflection preventive film can be a single layer of this polymer or a laminate of at least one layer of this polymer and at least one layer of another material having a refractive index different from that of this polymer. In order to enhance its reflection preventive capability, it is preferable to adjust refractive index of the polymer in a visible light region to 1.42 or lower, more preferably 1.4 or lower. As the fluorine content of the polymer increases, the refractive index becomes lower. With higher fluorine content, its adhesion to substrate tends to lower. In this case, it is possible to increase adhesion by using a reflection preventive film prepared by polymerizing a monomer that is represented by one of the general formulas (1)-(5) and that has an alcohol side chain in which R3 is a hydrogen. The thickness of the reflection preventive film may be varied depending on the refractive index of the substrate. It may be in a range of 50-200 nm.
It is possible to produce optical devices by using the polymer according to the present invention. For example, it is possible to produce an optical waveguide for wavelengths of 650-1,550 nm, preferably one for wavelengths of 850-1,550 nm that is relatively transparent to a light source used in semiconductor laser or in optical fiber for communication. It is possible to produce an optical waveguide (e.g., of a slab-type) by using the polymer for at least one of its core and cladding. For example, it is possible to produce an optical waveguide by a method comprising the sequential steps of (a) forming a lower cladding of a polymer according to the present invention; (b) coating the lower cladding with another polymer according to the present invention having a refractive index higher than that of the lower cladding; (c) partially irradiating the another polymer with light directly or using a mask to form a latent image; (d) removing the unirradiated portion of the another polymer by a solvent to form a core of a certain pattern; and (e) forming on the lower cladding an upper cladding of a polymer according to the present invention having a refractive index lower than that of the core in a manner that the core is embedded in the upper cladding, followed by heating or ultraviolet irradiation.
It is also possible to produce an optical waveguide by another similar method comprising the sequential steps of (a) forming a lower cladding layer; (b) forming thereon a core layer (flat film); (c) patterning the core layer using a photoresist; (d) forming a core ridge through reactive ion etching; and (e) forming thereon an upper cladding.
Generally speaking, optical devices are required to have heat resistance upon soldering since they are usually mounted on electrical devices or wiring substrates. According to the present invention, it is possible to provide the polymer with such heat resistance by (a) using a polymerizable monomer that is represented by one of the general formulas (1)-(5) and that has an alcohol side chain (hydroxyl group) in which R3 is a hydrogen and by (b) subjecting the hydroxyl group to a crosslinking reaction. A usable hardener for hardening the polymer is not particularly limited. Its examples are polyisocyanate and epoxy compounds, compounds containing a plurality of carboxyl groups in the molecule. It is possible to produce a negative-type light sensitive polymer by polymerizing the above polymerizable monomer in which R3 is an ester moiety prepared by an esterification between a side chain hydroxyl group and a (meth)acrylic acid or (meth)acrylic chloride. The resulting polymer can be used for various fields such as optical devices, reflection preventive film and resist.
It is possible to produce a novel resist composition by using the polymer according to the present invention. It is the most preferable to use this polymer for producing a positive-type resist composition. In fact, this resist composition contains (a) a polymer according to the present invention, of which solubility in alkali aqueous solution changes by the action of acid, and (b) an acid generator. This resist composition is preferably used, for example, for preparing semiconductors using a 193 nm ArF eximer laser or vacuum ultraviolet (typically 157 nm) F2 laser. In fact, the polymer, of which solubility in alkali aqueous solution changes by the action of acid, is characterized in that R2, R3 and R5 in the general formulas (1)-(5) are acid-labilized groups (i.e., groups to be labilized by acid). This polymer is not further particularly limited in its structure. This polymer can be prepared from a monomer (represented by one of the general formulas (1)-(5)) in which R2 has a tert-butyl structure as an acid-labilized group and in which its ester moiety is severed by an acid. Exemplary acid-labilized groups for R3 are tert-butyl group, tert-butoxycarbonyl group, open-chain and cyclic ether groups, and lactone group having a cyclic structure. The above polymer is insoluble or very slightly soluble in alkali aqueous solution prior to the activating energy ray irradiation. The activating energy ray irradiation, however, generates an acid from the acid generator. Then, the polymer is hydrolyzed by this acid and thereby becomes soluble in alkali aqueous solution.
The above-mentioned acid generator for a resist composition is not particularly limited. It can be suitably selected from acid generators for chemically amplified resists. Preferable examples of such acid generators are fluorine-containing sulfonic acid derivatives and fluorine-containing sulfonylimide derivatives. Preferable salts for the actual use as acid generators are bissulfonyldiazomethanes, nitrobenzyl derivatives, onium salts, halogen-containing triazine compounds, cyano group-containing oximesulfonate compounds, and other oximsulfonate compounds. The acid generator may be used in the form of a single compound or a mixture of at least two compounds. The content of the acid generator in the resist composition may be 0.5-20 parts by weight, relative to 100 parts by weight of the polymer. If it is less than 0.5 parts by weight, the resist composition may become insufficient in image forming capability. If it is greater than 20 parts by weight, it may become difficult to prepare a uniform solution of the resist composition. Thus, the resulting solution may become inferior in storage stability.
The above-mentioned resist composition according to the present invention can be used in conventional resist patterning methods, as exemplified in the following. Firstly, a solution of the resist composition is applied to a supporting member (e.g., silicon wafer) by spin coating or the like, followed by drying to form a photosensitive layer. Then, the photosensitive layer is exposed to an eximer laser light from an exposure apparatus through a desired mask pattern, followed by heating. Then, a development treatment is conducted by using, for example, an alkali aqueous solution such as 0.1-10 wt % tetramethylammonium hydroxide aqueous solution, thereby obtaining a resist pattern conforming to the mask pattern.
According to need, it is optional to add a miscible additive to the polymer. Examples of such additive are additional resins, quencher, plasticizer, stabilizer, coloring agent, surfactant, tackifier, leveling agent, deforming agent, compatibility enhancing agent, adhesion enhancing agent, and antioxidant.
The following nonlimitative Examples are illustrative of the present invention. Polymerizable monomers according to the present invention were synthesized by the following Synthesis Examples 1-6.